Question

How do you use the chain rule to differentiate `f(x)=(x^7-3x^2+15x^(-3/2))^6`?

Answer 1

`f’(x) = 6(x^7 +-3x2 + 15 x^ -(3/2))^5 * (7x^6 -6x + 45/(2sqrtx))`

Explanation:

`f(x) = ( x^7 - 3x^2 + 15x^-(3/2))^6`

`f’(x) = 6(x^7 -3x^2 + 15 x^-(3/2))^5 * (7x^6 - 6x + ((45/2) * x^-(1/2))`

`f’(x) = 6(x^7 +-3x2 + 15 x^ -(3/2))^5 * (7x^6 -6x + 45/(2sqrtx))`